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May17-09, 01:55 PM
P: 28
After some reading, I think that I may have a handle on it now - please correct me where I am wrong.

If someone asks the question 'what lies beyond the edge of the universe?'
it is kind of like a member of the flat earth society asking 'what lies beyond the edge of the earth?'
The difference being that the earths surface is just that - a surface, and the universe is a space.

I think that it would help non physicists like myself to clearly define which parts of the balloon
analogy is pertinent when trying to describe the mathematical model of the universe and which
parts are not.

I think it works like this:

The Balloon Analogy
"All points on the surface of a balloon get further away from each other as the balloon is inflated."

The pertinent parts of this analogy:
- The distance between any pair of points on the surface of the balloon increases with time because
new surface is being 'created' evenly (at the same rate) at all points on the surface between the two points.
- If one compares any two pairs of points on the surface of the balloon with differing distances between each point in the pair
- If the balloon was not expanding, a journey (at a finite speed) between the pair of points
that are further apart, would take longer than the journey between the pair of points
that are closer together.
- If the balloon is expanding, during the extra time that is taken to journey between the
pair of points that are further apart, more surface is created than would be
created during a journey between the closer pair of points.

The parts of this analogy that are not pertinent:
- The fact that a real balloon exists within a larger space, and as it expands it occupies more volume (thus a greater portion of this larger space) is not pertinent.
- The fact that in the case of a real balloon, the new surface is 'created' by thinning out the wall of the balloon and using that material to 'create' new surface is not pertinent.

Now, taking the pertinent lessons from the analogy, and ignoring the parts of the analogy that are not pertinent, think of the following scenario in the trimmed down analogy:
Imagine a very small ant that lives on the surface of the balloon, and imagine the balloon is very large in relation to the ant.
The ant's 'universe' is two dimensional (excluding time) as far as he (or she ) can see, but in his reality, it is actually curved, but the curvature is too gradual to be seen by him.
This two dimensional surface is all that exists in the trimmed down analogy.
We could say the following things:
- If the balloon wasn't expanding, the ant could start walking in any direction, and assuming the he lived long enough, he would end up at his starting point.
- If the balloon is expanding, the ant could only complete one complete one circumnavigation of the balloon, if he was able to cover at least as much surface as is created during the duration of his journey around the whole circumference of the balloon (added to the circumference of the balloon when he started his journey) at his maximum walking speed.
- If anyone asked the ant "what is beyond the edge of this universe?", the ant would have to reply "the universe".
- If anyone asked the ant "where is the edge of the universe" , the any would have to reply "there is no edge, but every point on the surface acts like an edge because new surface is created at every point at every time".
- If anyone asked the ant "is the universe infinite in size?", the ant would have to reply "no, but is has no boundary or edge".

How does this relate to our universe?
Our universe is not a 2 or 3 dimensional (excluding time) surface, but a 3 dimensional (excluding time) space.
If our universe wasn't expanding, we could take a rocket journey in any direction, and assuming the we lived long enough, we would end up at our point of departure.
Our universe is expanding though, so whether we could journey 'around' the universe and reach our starting point, is dependent on it's current size (distance that we would have to travel to reach our staring point again), and it's rate of expansion.
As far as I know, for the current values of:
- the size of the universe
- it's rate of expansion
even at the speed of light, we would still not be able to cover enough space to reach our starting point again even if we traveled for ever.
To be more verbose, the rate at which space is currently being created between our departure point at time t0 (start of our 'round trip' journey) and our departure / arrival point at time t1 (end of our 'round trip' journey) is greater than the rate at which one can cover distance at the speed of light.

Is this roughly correct, or is it still way off the mark?